Published: 25 April, 2006

Finding resonance of even the tiniest objects follows same steps

Is it possible to determine the resonance frequency of an object that has a diameter in nanometers in size (such as a cell)?

Good question. And the answer is, YES, it is certainly possible and has been the subject of intense study for quite some time - and still is! We constantly see mechanical oscillations in the world around us (musical instruments, children on swings, diving boards, etc.) So it is natural to wonder about oscillations of very small things (biological cells, small fibers and beams, etc.).

Well, the guidelines that define the behavior of damped, driven, harmonic oscillators are well established. A bit of terminology is unavoidable. Things can be driven by some form of energy (a person pushing a swing, electricity, shaking, etc) and they will respond by moving in a periodic motion (oscillations), and they will eventually stop moving because there is always friction absorbing the energy (damping). In addition, objects have favorite oscillation rates (natural frequencies) that they prefer. So if one pushes a child a little too often, or not often enough, the child will still swing, but not so high. On the other hand, if one pushes at just the right frequency, then the child will swing with higher and higher amplitude. This is the concept of resonance - drive a system at its natural frequency and you will receive a maximum response, and a happy child. We use the term Hertz (Hz), oscillations per second, to quantify the frequencies.

Uniformity of the object is also very important in determining its resonant frequency. If you shake a bowl of gelatin, you will see smooth vibrations, like water waves bouncing around. If you add fruit and marshmallows, the smooth vibrations will become more confused and harder to define. Now extend this discussion to a biological cell, which is an incredibly complex thing, full of many objects of varying densities, shapes, and sizes. They will still vibrate, but one would expect complex oscillation and a large number of resonance frequencies.

Even water, a relatively pure and simple material, shows some quite complex behavior, but it is certainly a good standard to use for this general discussion of how the resonant frequency changes as the size of an object changes. We can see oscillations in a bowl of water and estimate that they have a frequency of a few Hertz. Small water drops, about 1 millimeter in diameter, have a resonant frequency about 100 Hz, and approach 1000 Hz at about one half millimeter diameter. As structures get smaller and more complex, the frequencies rise, but the concept of a resonant frequency becomes more difficult to define.

Interestingly, small but simple structures like atoms can exhibit well behaved motion, and have been studied extensively for applications such as MRI (more precisely, Nuclear Magnetic Resonance Imaging). The MRI instrument detects tissue density in living things by mapping the presence of Hydrogen in water - tissue density is related to water density, which is related to Hydrogen density. We detect Hydrogen atoms by exciting them at their resonant frequency of 42,580,000 Hz.

In between the size of an atom and a drop of water, objects the size of living cells would be expected to vibrate mechanically at intermediate frequencies (10,000 - 500, 000 Hz). But also consider that other oscillations besides mechanical shaking are of interest in cells, including the rate of protein folding and unfolding, the rate at which nutrients enter and leave a cell, the rate at which life processes take place, and many others.

Because of the complexity of these small objects, the studies are a bit difficult, but the work goes on. And it is still based on the techniques noted above, that is, (1) excite the object with some form of energy (sound, mechanical vibrations, electromagnetic waves, changes in chemical concentration, etc), (2) observe the response, (3) develop a theory, and try to understand the world.